WASHINGTON (CNN) -- A Muslim family removed from an airliner Thursday after passengers became concerned about their conversation say AirTran officials refused to rebook them, even after FBI investigators cleared them of wrongdoing.

A Muslim family was removed from an AirTran flight after a conversation about the safest place to sit.

Atif Irfan said federal authorities removed eight members of his extended family and a friend after passengers heard them discussing the safest place to sit and misconstrued the nature of the conversation.

Irfan, a U.S. citizen and tax attorney, said he was "impressed with the professionalism" of the FBI agents who questioned him, but said he felt mistreated when the airline refused to book the family for a later flight.

AirTran Airways late Thursday said they acted properly and that the family was offered full refunds and can fly with AirTran again.

"The FBI agents actually cleared our names," said Inayet Sahin, Irfan's sister-in-law. "They went on our behalf and spoke to the airlines and said, 'There is no suspicious activity here. They are clear. Please let them get on a flight so they can go on their vacation,' and they still refused."

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The dispute occurred about 1 p.m. Thursday as AirTran flight 175 was preparing for takeoff from Reagan National Airport outside of Washington, D.C., on a flight destined for Orlando, Florida.

Atif Irfan, his brother, their wives, a sister and three children were headed to Orlando to meet with family and attend a religious conference.

"The conversation, as we were walking through the plane trying to find our seats, was just about where the safest place in an airplane is," Sahin said. "We were (discussing whether it was safest to sit near) the wing, or the engine or the back or the front, but that's it. We didn't say anything else that would raise any suspicion." Watch Muslims recount how they were kicked off plane »

The conversation did not contain the words "bomb," "explosion," "terror" or other words that might have aroused suspicion, Irfan said.

"When we were talking, when we turned around, I noticed a couple of girls kind of snapped their heads," said Sobia Ijaz, Irfan's wife. "I kind of thought to myself, 'Oh, you know, maybe they're going to say something.' It didn't occur to me that they were going to make it such a big issue."

Some time later, while the plane was still at the gate, an FBI agent boarded the plane and asked Irfan and his wife to leave the plane. The rest of the family was removed 15 or 20 minutes later, along with a family friend, Abdul Aziz, a Library of Congress attorney and family friend who was coincidentally taking the same flight and had been seen talking to the family.

After the FBI interviewed family members, it released them, Irfan said.

AirTran spokesman Tad Hutcheson said the incident began when some passengers reported hearing suspicious remarks by a woman and alerted flight attendants. Two federal air marshals, who were on board the flight, notified law enforcement about the security-related issue, AirTran said.

After the family and Aziz were taken for questioning, the remaining 95 passengers were taken off of the plane and rescreened, along with the crew and the baggage, AirTran said.

Irfan said he believes his family is owed an apology.

"Really, at the end of the day, we're not out here looking for money. I'm an attorney. I know how the court system works. We're basically looking for someone to say... 'We're apologizing for treating you as second-class citizens.'"

"We are proud Americans," Sahin said. "You know we decided to have our children and raise them here. We can very easily go anywhere we want in the world, but you know we love it here and we're not going to go away, no matter what."

Aziz said there is a "very strong possibility" he will pursue a civil rights lawsuit.

"I guess it's just a situation of guilt by association," Aziz said. "They see one Muslim talking to another Muslim and they automatically assume something wrong is going on."